The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints.
This theorem can be applied to determine the center of a given circle with straightedge and compass. Pick three points 
, 
and 
on the circle. Since the center is equidistant from all of
them, it lies on the bisector of segment 
and also on the bisector of segment 
, i.e., it is the intersection point of the two bisectors.
This construction is shown on a window pane by tutor Justin McLeod (Mel Gibson) to
his pupil Chuck Norstadt (Nick Stahl) in the 1993 film The
Man Without a Face.
